一类粮食酿酒化学反应的数学模型研究  

Studies on a Kind of Mathematical Model for Chemical Reactions of Grain Brewing

作　　者：王铁英[1] WANG Tieying(School for Policing Information Engineering and Cyber Security,People’s Public Security University of China,Beijing 100038,China)

机构地区：[1]中国人民公安大学警务信息工程与网络安全学院,北京100038

出　　处：《信阳师范学院学报（自然科学版）》2021年第1期1-4,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371306)。

摘　　要：研究了一类具有饱和反应速度的粮食酿酒化学反应的数学模型.应用常微分方程定性分析的方法主要讨论了平衡点的性态、系统解的一致有界性、正平衡点的全局渐近稳定性等,得到了系统不存在极限环的条件.理论结果表明,当参数满足一定的条件时,酿酒过程可以持续稳定地进行下去.A kind of mathematical model for chemical reactions of grain brewing with saturated reaction rate is analyzed.By using qualitative analytical methods of ordinary differential equations,the behaviour of equilibrium point,uniform boundedness of the solution,global asymptotic stability of the positive equilibrium of the system are discussed,and the conditions under which there is not limit cycles are obtained.The theoretical results show that if the parameters satisfy some conditions,then the process of brewing wine can be sustainable and steady.

关 键 词：粮食酿酒 一致有界性 全局渐近稳定性 极限环 

分 类 号：O175.13[理学—基础数学]